1. Field of the Invention
The present invention relates to carbon nanotube devices. More particularly, the present invention relates to resonator transistors fabricated from carbon nanotubes.
2. Description of the Related Art
Carbon nanotubes were discovered in the early 1990s as a product of arc-evaporation synthesis of fullerenes. Scientists have since determined that carbon nanotubes have extraordinary physical characteristics, and their potential use in many different applications has attracted much attention. For instance, carbon nanotubes have many attractive properties for high-quality mechanical resonators operating in the high frequency (HF) range through the microwave range.
A simple carbon nanotube resonator is shown in FIG. 1. The “clamped-clamped” resonator 100 includes carbon nanotube (CNT) 102 is clamped on both ends 104a and 104b and is biased by an electrode 106 with a voltage V. The capacitance of the resonator 100 can be represented by:
  Capacitance  =            2      ⁢      πɛ                                LN          ⁢                                          [                                    h              /              r                        +                          (                                                                    (                                          h                      /                      r                                        )                                    2                                -                1                            )                                )                          1          /          2                    ]      where h is the distance between the electrode 106 and the nanotube 102 (i.e., the size of the gap g) and r is the radius of the nanotube 102.
The CNT 102 is actuated by two mechanisms: electrostatic and charge injection.
Electrostatic actuation relates to a force applied normal to the nanotube axis represented by:Force=½*dC/dh*V2,Electrostatic actuation is described in detail in “Micromechanical Resonators for Oscillators and Filters,” C. T.-C. Nguyen, Proc. 1995 IEEE Ultrasonics Symposium, 489-99, 1995, the entire contents of which are incorporated herein by reference.
Charge injection actuation relates to axial strain, which can be represented by:δL/Lt≃δn/10
wherein δn=excess electrons/carbon atom. Motion normal to the tube axis is caused by buckling. Charge injection actuation is described in detail in “Carbon Nanotube Actuators,” R. H. Baughman et al., Science, 284, 1340-4, 1999 and “Charge-Induced Anisotropic Distortions of Semiconducting and Metallic Carbon Nanotubes,” Y. N. Gartstein et al., Phys. Reb. Lett., 89, July 2002, the contents of each are hereby incorporated by reference.
Both actuation mechanisms rely on the capacitance C between the nanotube 102 and the electrode 106. However, simple analysis reveals that for reasonably sized gaps g, the effective resistance of the nanotube resonator becomes very large.
FIG. 2A shows an LC circuit 200 modeling the resonator 100. In the circuit, the inductance L, the capacitance C and the resistance R can be represented by:
  L  =                    m                  η          2                    ⁢                          ⁢      C        =                                        η            2                    k                ⁢                                  ⁢        R            =                                    (            km            )                                1            /            2                                    Q          ⁢                                          ⁢                      η            2                              wherein m=effective mass, k=spring constant, η=V*dC/dh, and h is the distance from the electrode 106 to the nanotube 102 (i.e., gap g).
FIG. 2B shows the dynamic resistance of the resonator 100 in relation of the distance from the electrode 106 to the nanotube 102 (h). As shown, with small gaps (h<<radius of nanotube), the resonator 100 will have low dynamic resistance (ohms). However, a carbon nanotube resonator will have very large dynamic resistance when the electrode spacing is significantly greater than the nanotube radius. Therefore, a high impedance buffer amplifier will be needed at the output of the nanomechanical resonator to improve the signal strength available for conventional RF test equipment with 50 Ohm input impedance. The high impedance of the carbon nanotube resonators presents problems in practical devices and massive parallelism is being considered to bring the resistance into a manageable range.
Attempts to incorporate a carbon nanotube into a transistor have been made. FIG. 5A shows a diagram of a FET 500 having a carbon nanotube 502 grown into the channel thereof. FIG. 5B is a graph of its voltage-current characteristics of the transistor 500. This configuration was reported by International Business Machines Corporation and is published at “Single- and multi-wall carbon nanotube field-effect transistors”, R. Martel, T. Schmidt, H. R. Shea, T. Hertel and Ph. Avouris, Applied Physics Letters, 73, 17, pp2447-9, 1998, the contents of which are incorporated herein by reference.
This device 500 has the problem that the gate 504 extends over the whole surface beneath the source 506 and drain 508, which causes extremely high impedances. Therefore, the device 500 cannot operate even at moderate frequencies, let alone high frequencies.
In view of the foregoing, there is a need to develop new and improved carbon nanotube resonators and methods for making the same.